Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues n/a

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Spectral parameter

$R= 25.8102408383$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.172669765
4 0.5
5 0.447213595
6 0.829202743
7 0.0242815008
8 0.353553390
9 0.375154379
10 0.316227766
11 -0.709341649
12 0.586334882
13 -0.239292133
14 0.0171696139
15 0.524433862
16 0.250000000
17 -1.882893704
18 0.265274205
19 0.534993775
20 0.223606797
21 0.0284741819
22 -0.501580290
23 -1.325233530
24 0.414601371
25 0.200000000
26 -0.169205090
27 -0.732737567
28 0.0121407504
29 -0.347731088
30 0.370830740
31 -0.734200820
32 0.176776695
33 -0.831823506
34 -1.331406906
35 0.0108590173
36 0.187577189
37 0.355331801
38 0.378297726
39 -0.280610650
40 0.158113883
41 -0.505021374
42 0.0201342871
43 1.246725221
44 -0.354670824
45 0.167774139
46 -0.937081615
47 -1.716560582
48 0.293167441
49 -0.999410408
50 0.141421356
51 -2.208012519
52 -0.119646066
53 0.219785886
54 -0.518123702
55 -0.317227229
56 0.00858480695
57 0.627371025
58 -0.245883010
59 0.352085884
60 0.262216931
61 0.626065177
62 -0.519158378
63 0.00910931139
64 0.125000000
65 -0.107014695
66 -0.588188042
67 -0.819391851
68 -0.941446852
69 -1.554061293
70 0.00767848477
71 0.971776481
72 0.132637102
73 -1.123366171
74 0.251257526
75 0.234533953
76 0.267496887
77 -0.0172238798
78 -0.198421693
79 -0.663249672
80 0.111803398
81 -1.234413571
82 -0.357104038
83 1.308408828
84 0.0142370909
85 -0.842055663
86 0.881567858
87 -0.407773734
88 -0.250790145
89 -0.0218583960
90 0.118634231
91 -0.00581037214
92 -0.662616765
93 -0.860975103
94 -1.213791628
95 0.239256489
96 0.207300685
97 -0.0471156474
98 -0.706689877
99 -0.266112626
100 0.100000000
101 -0.216209231
102 -1.561300625
103 0.591027909
104 -0.0846025452
105 0.0127340412
106 0.155412090
107 1.009613862
108 -0.366368783
109 1.180162684
110 -0.224313525
111 0.416686860
112 0.00607037521
113 1.918408807
114 0.443618306
115 -0.592662451
116 -0.173865544
117 -0.0897714920
118 0.248962316
119 -0.0457194851
120 0.185415370
121 -0.496834423
122 0.442694932
123 -0.592223296
124 -0.367100410
125 0.0894427190
126 0.00644125586
127 1.554017644
128 0.0883883476
129 1.461996974
130 -0.0756708169
131 0.668452122
132 -0.415911753
133 0.0129904521
134 -0.579397534
135 -0.327690201
136 -0.665703453
137 0.315968643
138 -1.098887279
139 -1.662042115
140 0.00542950865
141 -2.012958696
142 0.687149740
143 0.169739877
144 0.0937885949
145 -0.155510070
146 -0.794339837
147 -1.171978363
148 0.177665900
149 1.029361086
150 0.165840548
151 -1.446940951
152 0.189148863
153 -0.706375804
154 -0.0121791222
155 -0.328344588
156 -0.140305325
157 -1.105483265
158 -0.468988341
159 0.257736263
160 0.0790569415
161 -0.0321783401
162 -0.872862206
163 -0.803409559
164 -0.252510687
165 -0.372002781
166 0.925184755
167 -1.693567773
168 0.0100671435
169 -0.942738697
170 -0.595423269
171 0.200705902
172 0.623362610
173 -0.274520023
174 -0.288339572
175 0.00485630017
176 -0.177335412
177 0.412883190
178 -0.0154562200
179 -1.237818245
180 0.0838870695
181 -1.463851192
182 -0.00410855354
183 0.734172038
184 -0.468540807
185 0.158909212
186 -0.608801334
187 1.335599490
188 -0.858280291
189 -0.0177427948
190 0.169179886
191 0.826512684
192 0.146583720
193 0.323070623
194 -0.0333157938
195 -0.125492897
196 -0.499705204
197 0.558609167
198 -0.188170042
199 -1.084030688
200 0.0707106781
201 -0.960940550
202 -0.152883013
203 -0.00776548658
204 -1.104006259
205 -0.225852424
206 0.417919842
207 -0.497236390
208 -0.0598230334
209 -0.381615065
210 0.00900432693
211 0.353903689
212 0.109892943
213 1.146498082
214 0.713904808
215 0.557552469
216 -0.259061851
217 -0.0209754362
218 0.834501037
219 -1.262814959
220 -0.158613614
221 0.487012763
222 0.294642104